JL writes:

None of these routes utilize Paddington Station, therefore travel from
any train leaving Paddington is not permitted. Therefore, the London
Underground must be used [1]. However, travel from Charing Cross,
Waterloo, Victoria, Canon Street, London Bridge or Any Thameslink is
permitted. As Reading is not a permitted routeing point, the Fare-
Check rule does not come into play.

However, travel from Paddington to Clapham Jn via Reading and either
Basingstoke or Staines would be allowed on a Basingstoke (and probably
other stations on the SWT main line) to London Stations season, as
travel Basingstoke-Reading-Paddington and
Basingstoke-Reading-Staines-Clapham Jn are permitted routes. Season
tickets allow unlimited travel between intermediate stations on all
permitted routes.